Finite Group Databasebeta

← #21448867

Subgroups — #21448867

Order 7808.

716 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519749C211yesmaximal, characteristic
2C2×D4×Dic61C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D61C211yesmaximal, characteristic, complemented
4#16839654C211yesmaximal, characteristic, complemented
5#16839650C211yesmaximal, characteristic, complemented
6#16839649C211yesmaximal, characteristic, complemented
7#16839644C211yesmaximal, characteristic, complemented
8#16839639C211yesmaximal, characteristic, complemented
9#16839639C211yesmaximal, characteristic, complemented
10#16839638C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
13#16839609C211yesmaximal, characteristic, complemented
14C2×#14519684C211yesmaximal, characteristic, complemented
15C61×#386C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C23×Dic61C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20C23×Dic61C2211yescharacteristic
21C22×C4×D61C2211yescharacteristic
22#14519749C418yescomplemented
23D4×Dic61—24no—
24C4×C22⋊D61—24no—
25C2×C4⋊Dic61C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×C4×Dic61C2211yescharacteristic
36C2×C4×Dic61C2211yescharacteristic
37C2×C4×Dic61C2211yescharacteristic
38C2×C4×Dic61C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47C22×D4×C61C2211yescharacteristic
48C23×C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53#95×C61C2211yescharacteristic
54C24×C61C2311yescharacteristic
55C24×C61C2311yescharacteristic
56C23×D61C2311yescharacteristic
57C2×D4×C61—22no—
58C2×D4×C61—22no—
59C2×D4×C61C2×C414yescomplemented
60C22×C4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61—41no—
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—22no—
69C2×C22⋊D61—22no—
70C2×C22⋊D61—41no—
71C2×C22⋊D61—41no—
72C2×C22⋊D61C2×C414yescomplemented
73C2×C22⋊D61C2×C414yescomplemented
74C22×Dic61—22no—
75C22×Dic61—22no—
76C22×Dic61—22no—
77C22×Dic61—22no—
78C22×Dic61—41no—
79C22×Dic61—41no—
80C22×Dic61—41no—
81C22×Dic61—41no—
82C22×Dic61C2×C414yescomplemented
83C22×Dic61C2311yescharacteristic
84C22×Dic61C2311yescharacteristic
85C22×Dic61C2311yescharacteristic
86C22×Dic61C2311yescharacteristic
87C22×Dic61C2311yescharacteristic
88C22×Dic61C2311yescharacteristic
89C22×Dic61C2311yescharacteristic
90C2×C4×D61—22no—
91C2×C4×D61—22no—
92C2×C4×D61—41no—
93C22⋊C4×C61—22no—
94C22⋊C4×C61—22no—
95C22⋊C4×C61—41no—
96C22⋊Dic61—22no—
97C22⋊Dic61C2×C414yescomplemented
98C22⋊Dic61D414yescomplemented
99#11758198—22no—
100#11758198—22no—
101#11758198—41no—
102#11758198C2×C414yescomplemented
103C4⋊Dic61—22no—
104#11758196—22no—
105#11758196C2×C414yescomplemented
106C4×Dic61—22no—
107C4×Dic61—22no—
108C4×Dic61—41no—
109C4×Dic61—41no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61C22×C412yes—
121C23×C61C22×C412yes—
122C23×C61C2×D412yes—
123C23×C61#4112yes—
124C23×C61C2411yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61C22×C412yes—
132D4×C61—28no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—44no—
147C2×C4×C61C22×C412yes—
148C2×C4×C61#4112yes—
149C22⋊D61—28no—
150C22⋊D61—44no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—44no—
167C2×Dic61—44no—
168C2×Dic61—44no—
169C2×Dic61C22×C412yes—
170C2×Dic61C22×C412yes—
171C2×Dic61C22×C412yes—
172C2×Dic61C2×D412yes—
173C2×Dic61C2×D412yes—
174C2×Dic61#4112yes—
175C4×D61—44no—
176C22×C61—22no—
177C22×C61—22no—
178C22×C61—22no—
179C22×C61—22no—
180C22×C61—22no—
181C22×C61—22no—
182C22×C61—22no—
183C22×C61—22no—
184C22×C61—22no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61C4×D414yes—
190C22×C61C23×C411yescharacteristic
191C22×C61C22×D411yescharacteristic
192C22×C61C2×#4111yescharacteristic
193C22×C61C2×#4111yescharacteristic
194C22×C61C2×#4111yescharacteristic
195C22×C61H(5,𝔽2)11yescharacteristic
196C22×C61H(5,𝔽2)11yescharacteristic
197C2×D61—22no—
198C2×D61—22no—
199C2×D61—22no—
200C2×D61—41no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—41no—
204C4×C61—22no—
205C4×C61—22no—
206C4×C61—41no—
207C4×C61—41no—
208C4×C61—41no—
209Dic61—22no—
210Dic61—22no—
211Dic61—22no—
212Dic61—22no—
213Dic61—22no—
214Dic61—22no—
215Dic61—41no—
216#2364—611nomaximal, Sylow
217C2×C61—24no—
218C2×C61—42no—
219C2×C61C2×C4×D411yescharacteristic
220C2×C61C4×#4111yescharacteristic
221C2×C61#51811yescharacteristic
222C2×C61#54611yescharacteristic
223C2×C61#54611yescharacteristic
224C2×C61#55311yescharacteristic
225C2×C61#55311yescharacteristic
226D61—42no—
227C2×#121—611no—
228C2×C4×D4—611no—
229C2×C4×D4—611no—
230#388—611no—
231#388—611no—
232#387—611no—
233#387—611no—
234#386—611no—
235#386—611no—
236#386—611no—
237#386D6111yescharacteristic, complemented
238C4×C22⋊C4—611no—
239C4×C22⋊C4—611no—
240C4×C22⋊C4—611no—
241C2×#95—611no—
242C61#236411yescharacteristic, complemented, Sylow
243C22×D4—611no—
244C22×D4—611no—
245C22×D4C2×D6111yescharacteristic
246C23×C4—611no—
247C23×C4—611no—
248C23×C4—611no—
249C23×C4—611no—
250C23×C4C2×D6111yescharacteristic
251#121—618no—
252C4×D4—1224no—
253C4×D4—1224no—
254C2×C4⋊C4—611no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4—611no—
257C2×C22⋊C4—611no—
258C2×C22⋊C4—611no—
259C2×C22⋊C4—611no—
260C2×C22⋊C4—611no—
261C2×C22⋊C4—611no—
262C2×C22⋊C4—611no—
263C2×C22⋊C4—611no—
264C2×C22⋊C4C2×D6111yescharacteristic
265C2×C22⋊C4C2×D6111yescharacteristic
266C2×C22⋊C4C2×D6111yescharacteristic
267C2×C42—611no—
268C2×C42—611no—
269C2×C42—611no—
270C2×C42—611no—
271#95—611no—
272#95—611no—
273#95—611no—
274#95—611no—
275#95—611no—
276#95—611no—
277#95—611no—
278#95—611no—
279#95C2×D6111yescharacteristic
280#95C2×D6111yescharacteristic
281C24—611no—
282C24C22×D6111yescharacteristic
283C24C22×D6111yescharacteristic
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—614no—
287C2×D4—614no—
288C2×D4—1222no—
289C2×D4—1222no—
290C2×D4—2441no—
291C2×D4—2441no—
292C2×D4C4×D6114yescomplemented
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—41no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—611no—
302C22×C4—614no—
303C22×C4—611no—
304C22×C4—1222no—
305C22×C4—1222no—
306C22×C4—1222no—
307C22×C4—1222no—
308C22×C4—1222no—
309C22×C4—1222no—
310C22×C4—2441no—
311C22×C4—2441no—
312C22×C4—2441no—
313C22×C4—2441no—
314C22×C4—2441no—
315C22×C4C22×D6111yescharacteristic
316C22×C4C22×D6111yescharacteristic
317C22×C4C22×D6111yescharacteristic
318C22×C4C22×D6111yescharacteristic
319C22×C4C22×D6111yescharacteristic
320C4⋊C4—614no—
321C4⋊C4—1222no—
322C4⋊C4—1222no—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—41no—
326C22⋊C4—614no—
327C22⋊C4—614no—
328C22⋊C4—614no—
329C22⋊C4—1222no—
330C22⋊C4—1222no—
331C22⋊C4—1222no—
332C22⋊C4—2441no—
333C42—1222no—
334C42—1222no—
335C42—2441no—
336C42—2441no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—612no—
348C23—1221no—
349C23—1221no—
350C23—1221no—
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23C2×C4×D6112yes—
355C23C2×C4×D6112yes—
356C23D4×D6112yes—
357C23#1175822412yes—
358C23C23×D6111yescharacteristic
359D4—28no—
360D4—1228no—
361D4—2444no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—44no—
376C2×C4—612no—
377C2×C4—612no—
378C2×C4—612no—
379C2×C4—612no—
380C2×C4—612no—
381C2×C4—612no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—1221no—
389C2×C4—1221no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—2444no—
398C2×C4—2444no—
399C2×C4—2444no—
400C2×C4—2444no—
401C2×C4C2×C4×D6112yes—
402C2×C4#1175822412yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—22no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—1222no—
417C22—1222no—
418C22—1222no—
419C22—2441no—
420C22—2441no—
421C22—2441no—
422C22—2441no—
423C22#1451973714yes—
424C22C22×C4×D6111yescharacteristic
425C22C2×D4×D6111yescharacteristic
426C22#41×D6111yescharacteristic
427C22C2×#1175822411yescharacteristic
428C22C2×#1175822411yescharacteristic
429C22#1451982211yescharacteristic
430C22#1451982311yescharacteristic
431C4—22no—
432C4—22no—
433C4—41no—
434C4—41no—
435C4—41no—
436C4—1222no—
437C4—1222no—
438C4—1222no—
439C4—1222no—
440C4—1222no—
441C4—1222no—
442C4—2441no—
443C2—24no—
444C2—42no—
445C2—2442no—
446C2C2×#1451973711yescharacteristic
447C2C4×#1175822411yescharacteristic
448C2#1684023411yescharacteristic
449C2#1684039911yescharacteristic
450C2#1684040411yescharacteristic
451C2#1684045511yescharacteristic
452C2#1684046411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#386C2
socleC23×C61C24
hypercenter#386D61
hypocenterC61#2364
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×D4×Dic61C2semidirect
3. C2×C4×C22⋊D61C2semidirect
4. #16839654C2semidirect
5. #16839650C2semidirect
6. #16839649C2semidirect
7. #16839644C2semidirect
8. #16839639C2semidirect
9. #16839639C2semidirect
10. #16839638C2semidirect
11. C22⋊C4×Dic61C2semidirect
12. C22⋊C4×Dic61C2semidirect
13. #16839609C2semidirect
14. C2×#14519684C2semidirect
15. C61×#386C2semidirect
22. #14519749C4semidirect
59. C2×D4×C61C2×C4semidirect
72. C2×C22⋊D61C2×C4semidirect
73. C2×C22⋊D61C2×C4semidirect
82. C22×Dic61C2×C4semidirect
97. C22⋊Dic61C2×C4semidirect
98. C22⋊Dic61D4semidirect
102. #11758198C2×C4semidirect
105. #11758196C2×C4semidirect
237. #386D61semidirect
242. C61#2364semidirect
292. C2×D4C4×D61semidirect